On the basis of available data with regard to the chemical and physical properties of the "substrate" luciferin (LH2) and enzyme, luciferase (A), and of kinetic data derived both from the reaction in extracts of Cypridina, and from the luminescence of intact bacteria, the fundamental reactions involved in the phenomenon of bioluminescence have been schematized. These reactions provide a satisfactory basis for interpreting the known characteristics of the system, as well as the theoretical chemistry with regard to the control of its over-all velocity in relation to various factors. These factors, here studied experimentally wholly with bacteria, Photobacterium phosphoreum in particular, include pH, temperature, pressure, and the drugs sulfanilamide, urethane, and alcohol, separately and in relation to each other. Under steady state conditions of bacterial luminescence, with excess of oxidizable substrate and with oxygen not limiting, the data indicate that the chief effects of these agents center around the pace setting reactions, which may be designated by the equation:

A + LH2 → ALH2

following which light emission is assumed proportional to the amount of the excited molecule, AL*.

The relation between pH and luminescence intensity varies with (a), the buffer mixture and concentration, (b), the temperature, and (c), the hydrostatic pressure.

At an optimum temperature for luminescence of about 22° C. in P. phosphoreum, the effects of increasing or decreasing the hydrogen ion concentration are largely reversible over the range between pH 3.6 and pH 8.8. The relation between luminescence intensity and pH, under the experimental conditions employed, is given by the following equation, in which I1 represents the maximum intensity, occurring about pH 6.5; I2 the intensity at any other given pH; K5 the equilibrium constant between hydrogen ions and the AL-; and K6 the corresponding constant with respect to hydroxyl ions:

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The value of K5, as indicated by the data, amounts to 4.84 x 104, while that of K6 amounts to 4.8 x 105.

Beyond the range between approximately pH 3.8 and 8.8, destructive effects of the hydrogen and hydroxyl ions, respectively, were increasingly apparent. By raising the temperature above the optimum, the destructive effects were apparent at all pH, and the intensity of the luminescence diminished logarithmically with time. With respect to pH, the rate of destruction of the light-emitting system at temperatures above the optimum was slowest between pH 6.5 and 7.0, and increased rapidly with more acid or more alkaline reactions of the medium.

The reversible effects of slightly acid pH vary with the temperature in the manner of an inhibitor (Type I) that acts independently of the normal, reversible denaturation equilibrium (K1) of the enzyme. The per cent inhibition caused by a given acid pH in relation to the luminescence intensity at optimum pH, is much greater at low temperatures, and decreases as the temperature is raised towards the optimum temperature. The observed maximum intensity of luminescence is thus shifted to slightly higher temperatures by increase in (H+).

The apparent activation energy of luminescence is increased by a decrease in pH. The value of ΔH‡ at pH 5.05 was calculated to be 40,900 calories, in comparison with 20,700 at a pH of 6.92. The difference of 20,200 is taken to represent an estimate of the heat of ionization of ALH in the activation process, and compares roughtly with the 14,000 calories estimated for the same process, by analyzing the data from the point of view of hydrogen ions as an inhibitor. The decreasing temperature coefficient for luminescence in proceeding from low temperatures towards the optimum is accounted for in part by the greater degree of ionization of ALH.

At the optimum temperature and acid reactions, pressures up to about 500 atmospheres retard the velocity of the luminescent oxidation. At the same temperature, with decrease in hydrogen ion concentration, the pressure effect is much less, indicating a considerable volume increase in the process of ionization and activation.

In the extremely alkaline range, beyond pH 9, luminescence is greatly reduced, as compared with the intensity at neutrality, and under these conditions pressure causes a pronounced increase in intensity, presumably by acting upon the reversible denaturation equilibrium of the protein enzyme, A.

Sulfanilamide, in neutral solutions, acts on luminescence in a manner very much resembling that of hydrogen ions at acidities between pH 4.0 and pH 6.5. Like the hydrogen ion equilibrium, the sulfanilamide equilibrium involves a ratio of approximately one inhibitor molecule to one enzyme molecule. The heat of reaction amounts to about 11,600 calories or more in a reversible combination that evidently evolves heat. Like the action of H ions, sulfanilamide causes a slight shifting of maximum luminescence intensity in the direction of higher temperatures, and an increase in the energy of activation.

The effect of sulfanilamide on the growth of broth cultures of eight species of luminous bacteria indicates that there is no regular relationship among the different organisms between the concentration of the drug that prevents growth, and that which prevents luminescence in the cells which develop in the presence of sulfanilamide. p-Aminobenzoic acid (PAB) antagonizes the sulfanilamide inhibition of growth in luminous bacteria, and the cultures that develop are luminous. When (PAB) is added to cells from fully developed cultures, it has no effect on luminescence, or causes a slight inhibition, depending on the concentration. With luminescence partly inhibited by sulfanilamide, the addition of PAB has no effect, or has an inhibitory effect which adds to that caused by sulfanilamide. Two different, though possibly related, enzyme systems thus appear to limit growth and luminescence, respectively. The possible mechanism through which both the inhibitions and the antagonism take place is discussed.

The irreversible destruction of the luminescent system at temperatures above that of the maximum luminescence, in a medium of favorable pH to which no inhibitors have been added, proceeds logarithmically with time at both normal and increased hydrostatic pressures. Pressure retards the rate of the destruction, and the analysis of the data indicates that a volume increase of roughly 71 cc. per gm. molecule at 32° C. takes place in going from the normal to the activated state in this reaction. At normal pressure, the rate of destruction has a temperature coefficient of approximately 90,000 calories, or about 20,000 calories more than the heat of reaction in the reversible denaturation equilibrium. The data indicate that the equilibrium and the rate process are two distinct reactions. The equation for luminescence intensity, taking into account both the reversible and irreversible phases of the reaction is given below. In the equation b is a proportionality constant; k' the rate constant of the luminescent reaction; A0 the total luciferase; A0i the total initial luciferase at time t equals 0; kn the rate constant for the destruction of the native, active form of the enzyme; kd the rate constant for the destruction of the reversibly denatured, inactive form; t the time; and the other symbols are as indicated above:

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For reasons cited in the text, kn evidently equals kd.

Urethane and alcohol, respectively, act in a manner (Type II) that promotes the breaking of the type of bonds broken in both the reversible and irreversible reactions and so promotes the irreversible denaturation. This result is in contrast to the effects of sulfanilamide, which at appropriate concentrations may give rise to the same initial inhibition as that caused by urethane, but remains constant with time.

The inhibition caused by urethane and alcohol, respectively, increases as the temperature is raised. As a result, the apparent optimum is shifted to lower temperatures, and the activation energy for the over-all process of luminescence diminishes. An analysis for the approximate heat of reaction in the equilibrium between these drugs and the enzyme, indicates 65,000 calories for urethane, and 37,000 for alcohol. A similar analysis with respect to the effect of hydroxyl ions as the inhibitor gives 60,300 calories.

The effects of alcohol and urethane are sensitive to hydrostatic pressure. Moderate inhibitions at optimum temperature and pH, caused by relatively small concentrations of either drug, are completely abolished by pressures of 3,000 to 4,000 pounds per square inch.

At optimum temperature and pH, increasing concentrations of alcohol caused the apparent optimum pressure for luminescence to shift markedly in the direction of higher pressures. Analysis of the data with respect to concentration of alcohol at different pressures indicated that the ratio of alcohol to enzyme molecules amounted to approximately 4, at 7,000 pounds, but only about 2.8 at normal pressures. This phenomenon was taken to indicate that more than one equilibrium is established between the alcohol and the protein. A similar interpretation was suggested in connection with the fact that analysis of the relation between concentration of urethane and amount of inhibition at different temperatures also indicated a ratio of urethane to enzyme molecules that increased with temperature in the equilibria involved.

Analysis of the data with respect to pressure and the inhibition caused by a given concentration of alcohol at different temperatures indicated that the volume change involved in the combination of alcohol with the enzyme must be very small, while the actual effect of pressure is apparently mediated through the reversible denaturation of the protein enzyme, which is promoted by alcohol, urethane, and drugs of similar type.

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